Browsing by Author "Martins, Nuno"
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- 18FDG PET/CT in the qualitative and quantitative evaluation of the therapeutic response in Hodgkin’s lymphomaPublication . Martins, Nuno; Hunter, James; Vaz, Tânia; Dizdarevic, Sabina
- Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approachPublication . Sardanyés, Josep; Rodrigues, Carla; Januário, Cristina; Martins, Nuno; Gil-Gómez, Gabriel; Duarte, JorgeIn this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems – the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.
- Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic modelPublication . Duarte, Jorge; Januário, Cristina; Martins, Nuno; Rogovchenko, Svitlana; Rogovchenko, YuriyDespite numerous studies of epidemiological systems, the role of seasonality in the recurrent epidemics is not entirely understood. During certain periods of the year incidence rates of a number of endemic infectious diseases may fluctuate dramatically. This influences the dynamics of mathematical models describing the spread of infection and often leads to chaotic oscillations. In this paper, we are concerned with a generalization of a classical Susceptible–Infected–Recovered epidemic model which accounts for seasonal effects. Combining numerical and analytic techniques, we gain new insights into the complex dynamics of a recurrent disease influenced by the seasonality. Computation of the Lyapunov spectrum allows us to identify different chaotic regimes, determine the fractal dimension and estimate the predictability of the appearance of attractors in the system. Applying the homotopy analysis method, we obtain series solutions to the original nonautonomous SIR model with a high level of accuracy and use these approximations to analyze the dynamics of the system. The efficiency of the method is guaranteed by the optimal choice of an auxiliary control parameter which ensures the rapid convergence of the series to the exact solution of the forced SIR epidemic model.
- Chaos and crises in a model for cooperative hunting: A symbolic dynamics approachPublication . Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyes, JosepIn this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K, C-0) and (K, sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K-c decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.
- A chaotic bursting-spiking transition in a pancreatic beta-cells system: observation of an interior glucose-induced crisisPublication . Duarte, Jorge; Januário, Cristina; Martins, NunoNonlinear systems are commonly able to display abrupt qualitative changes (or transitions) in the dynamics. A particular type of these transitions occurs when the size of a chaotic attractor suddenly changes. In this article, we present such a transition through the observation of a chaotic interior crisis in the Deng bursting-spiking model for the glucose-induced electrical activity of pancreatic _-cells. To this chaos-chaos transition corresponds precisely the change between the bursting and spiking dynamics, which are central and key dynamical regimes that the Deng model is able to perform. We provide a description of the crisis mechanism at the bursting-spiking transition point in terms of time series variations and based on certain amplitudes of invariant intervals associated with return maps. Using symbolic dynamics, we are able to accurately compute the points of a curve representing the transition between the bursting and spiking regimes in a biophysical meaningfully parameter space. The analysis of the chaotic interior crisis is complemented by means of topological invariants with the computation of the topological entropy and the maximum Lyapunov exponent. Considering very recent developments in the literature, we construct analytical solutions triggering the bursting-spiking transition in the Deng model. This study provides an illustration of how na integrated approach, involving numerical evidences and theoretical reasoning within the theory of dynamical systems, can directly enhance our understanding of biophysically motivated models.
- Contributo para o estabelecimento de níveis de referência de diagnóstico locais em tomografia computorizada nos exames de crânio e tórax em adultosPublication . Torres, Ana; Rodrigues, Dulce; Lança, Luís; Machado, Nuno; Martins, NunoAtualmente a Tomografia Computorizada (TC) é o método de imagem que mais contribui para a dose coletiva resultante de exposições médicas. Este estudo pretende determinar os valores de Índice de Dose de TC (CTDI) e produto dose-comprimento (DLP) para os exames de crânio e tórax em adultos num equipamento de TC multidetetores; e efetuar uma análise objetiva e subjetiva da qualidade da imagem. Determinaram-se os valores de CTDI e DLP utilizando uma câmara de ionização e fantomas de crânio e tórax. Efetuou-se ainda uma análise objetiva e subjetiva da qualidade da imagem com o fantoma Catphan® 500 e observadores, respetivamente. Os resultados obtidos foram superiores relativamente às Guidelines europeias no protocolo de crânio (CTDIvol = 80,13 mGy e DLP = 1209,22 mGy.cm) e inferiores no protocolo de tórax (CTDIvol = 8,37 mGy e DLP = 274,71 mGy.cm). Na análise objetiva da qualidade da imagem, à exceção da resolução de baixo contraste no protocolo de crânio, todos os outros critérios analisados estavam em conformidade com a legislação. Na análise subjetiva da qualidade da imagem existiu uma diferença estatisticamente significativa entre as classificações atribuídas pelos observadores às imagens nos parâmetros avaliados (p = 0,000-0,005).
- Controling delayed transitions with applications to prevent single species extinctionsPublication . Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, JosepA new method is proposed to control delayed transitions towards extinction in single population theoretical models with discrete time undergoing saddle-node bifurcations. The control method takes advantage of the delaying properties of the saddle remnant arising after the bifurcation, and allows to sustain populations indefinitely. Our method, which is shown to work for deterministic and stochastic systems, could generally be applied to avoid transitions tied to one-dimensional maps after saddle-node bifurcations.
- Controlling infectious diseases: the decisive phase effect on a seasonal vaccination strategyPublication . Duarte, Jorge; Januário, Cristina; Martins, Nuno; Seoane, Jesús M.; SANJUAN, MIGUEL A. F.The study of epidemiological systems has generated deep interest in exploring the dynamical complexity of common infectious diseases driven by seasonally varying contact rates. Mathematical modeling and field observations have shown that, under seasonal variation, the incidence rates of some endemic infectious diseases fluctuate dramatically and the dynamics is often characterized by chaotic oscillations in the absence of specific vaccination programs. In fact, the existence of chaotic behavior has been precisely stated in the literature as a noticeable feature in the dynamics of the classical Susceptible-Infected-Recovered (SIR) seasonally forced epidemic model. However, in the context of epidemiology, chaos is often regarded as an undesirable phenomenon associated with the unpredictability of infectious diseases. As a consequence, the problem of converting chaotic motions into regular motions becomes particularly relevant. In this article, we consider the so-called phase control method applied to the seasonally forced SIR epidemic model to suppress chaos. Interestingly, this method of controlling chaos has a clear meaning as a weak perturbation on a seasonal vaccination strategy. Numerical simulations show that the phase difference between the two periodic forces - contact rate and vaccination - plays a very important role in controlling chaos.
- Copper(II) and iron(III) complexes with arylhydrazone of ethyl 2-cyanoacetate or formazan ligands as catalysts for oxidation of alcoholsPublication . Martins, Nuno; Mahmudov, Kamran T.; Guedes Da Silva, M. Fátima C.; Martins, Luisa; Pombeiro, ArmandoThe aquasoluble [Cu(1 kappa N,O-2:2 kappa O-HL1)(S)](2) [S = CH3OH (1), (CH3)(2)NCHO (2)] and [Cu(kappa N-HL1)(en)(2)]center dot CH3OH center dot H2O (3) Cu-II complexes were prepared by the reaction of Cu-II nitrate hydrate with the new ligand (E/Z)-4-(2-(1-cyano-2-ethoxy-2-oxoethylidene)hydrazinyl)-3-hydroxybenzoic acid (H3L1), in the presence (for 3) or absence (for 1 and 2) of ethylenediamine (en), while the Fe-III complex [Fe(kappa N-3-HL2)(2)] (4) was isolated by treatment of iron(III) chloride hexahydrate with the new ligand (1E,1E)-N',2-di(1H-1,2,4-triazol-3-yl)diazenecarbohydrazonoyl cyanide (H3L2), and characterized by elemental analysis, IR spectroscopy and single crystal X-ray diffraction. Cooperative E,Z -> E isomerization of H3L1, induced by coordination and ionic interactions, occurs upon interaction with Cu-II in the presence of en. Complexes 1-4 act as catalyst precursors for the solvent-free microwave (MW) assisted selective oxidation of primary or secondary alcohols and diols to the corresponding aldehydes, ketones and diketones, respectively, with yields in the 5-99% range (TONs up to 4.96 x 10(2)) after 60 min of MW irradiation at 120 degrees C. The influence of temperature, time and organic radicals was studied and also the regioselective oxidation of the catalytic systems involving the primary and secondary alcohols.
- DNA and BSA binding and cytotoxic properties of copper(II) and iron(III) complexes with arylhydrazone of ethyl 2-cyanoacetate or formazan ligandsPublication . Martins, Nuno; Sellamuthu, Anbu; Mahmudov, Kamran; Ravishankaran, Rajendran; Guedes Da Silva, M. Fátima C.; Martins, Luisa; Karande, Anjali A.; Pombeiro, ArmandoSeveral known water soluble [Cu(1N,O2:2O-HL1)(S)]2 [S = CH3OH (1), (CH3)2NCHO (2)] and [Cu(N-HL1)(en)2]∙CH3OH∙H2O (3) CuII complexes were prepared by reaction of CuII nitrate hydrate with the new (E/Z)-4-(2-(1-cyano-2-ethoxy-2-oxoethylidene)hydrazinyl)-3-hydroxybenzoic acid (H3L1), in the presence (for 3) or absence (for 1 and 2) of ethylenediamine (en), while the FeIII complex [Fe(N3-HL2)2] (4) was synthesized by treatment of iron(III) chloride hexahydrate with the new (1E,1E)-N',2-di(1H-1,2,4-triazol-3-yl)diazenecarbohydrazonoyl cyanide (H3L2). The interaction of calf thymus DNA (CT DNA) and bovine serum albumin (BSA protein) with complexes 1−4 has been investigated by absorption and fluorescence titration methods. The observed DNA binding constants, number of DNA binding sites (s ≤ 1) for complexes and viscosity data suggest that the intercalative mode of binding to CT DNA. All the complexes show good binding propensity to the BSA, giving KBSA values of 0.97(±0.10) × 106 (1), 1.19(±0.09) × 106 (2), 0.50(±0.01) × 106 (3) and 1.06(±0.08) × 106 M-1 (4). The in vitro anti-proliferative study establishes the anticancer potency of complexes 1−4 and cisplatin against the human cervical (HeLa) and breast (MCF7) cancer cell lines; noncancer breast epithelial (MCF10) cells were also investigated. The observed IC50 values of the complexes 1 (8.3, 11.9 and 44.8 μM), 2 (7.0, 7.1 and 35.6 μM), 3 (18.1, 20.4 and 58.8 μM), 4 (13.2, 15.1 and 79.4 μM) and cisplatin (4.02, 3.42 and 89.5 μM) against the HeLa, MCF7 and MCF-10a cells, respectively, suggest that 2 can be explored further as a potential anticancer drug.
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